A Pokémon's Characteristic is determined by the remainder of its highest IV divided by 5 (known as modulo operation in programming). Since it is built this way, Pokémon transferred from the games of Generation III via Pal Park have a Characteristic without their stats being changed.

Note that having a certain Characteristic does not necessarily imply that the highest possible value for an IV is present. A Pokémon with an "Alert to sounds" Characteristic could have a 6 in Speed (and thus very low IVs across all of its stats since none could be higher than 6) instead of a 31 in Speed.

Mistranslations

In Generations IV and V, two of the Characteristics were not properly translated from the Japanese releases. The HP Characteristics corresponding to IVs of 1 and 2 were accidentally replaced by the Characteristics corresponding to IVs of 2 and 3, respectively. So, rather than the HP Characteristics being ordered "Takes plenty of siestas", "Nods off a lot" (i.e., "Often dozes off"), and "Scatters things often" as they should have been, they were ordered "Often dozes off", "Often scatters things", "Scatters things often" (note that the last two are different, but only trivially).

Ties

In the event of a tie in highest IVs, the IV that determines the Pokémon's Characteristic is decided in the following manner:

Start with the Pokémon's personality value (Generation IV and V) or encryption constant (Generation VI). Take that value modulo 6. The result is an index number of a stat in this order: HP, Attack, Defense, Speed, Special Attack, Special Defense. In the event of a tie in IVs, the first IV checked is the IV corresponding to that index number. If that IV is not part of the tie, the game moves on to the next index number in the aforementioned order. If it goes past 5 (Special Defense), it wraps around back to 0 (HP). When the game finds an IV that is part of the tie, that is the IV that will determine the Characteristic displayed.

Examples

Since its highest IV is 29 in Speed, its Characteristic will be "Quick to flee."

A Ditto has the following IVs and a personality value of 1467750821 in base 10:

Hit Points

Attack

Defense

Speed

Sp.Attack

Sp.Defense

8

0

0

17

17

10

Since its highest IV is 17 in both Speed and Special Attack, the result of 1467750821 mod 6, or 5, is used to check against the IV in Special Defense. Since the Special Defense is not part of the tie, the game moves on and wraps back until it reaches Speed, which is part of the tie. Its Characteristic will be "Impetuous and silly."